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Talk

Pablo Sánchez-Peralta (Universidad Autónoma de Madrid): The strong Atiyah conjecture for graph of groups via universal localizations

Abstract

The study of the rationality of the $L^2$-Betti numbers of a countable discrete group has led to the development of a rich theory in $L^2$-homology with deep implications in structural properties of the groups. For decades almost nothing has been known about the general question of whether the strong Atiyah conjecture passes to free products of groups or not. In this talk, we will confirm that the strong Atiyah conjecture is stable under the graph of groups construction provided that the edge groups are finite. We will also discuss how universal localizations can be used to describe those division rings.

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